A design study for the extraction system of the 3rd Generation super conducting ECR ion source at LBNL is presented. The magnetic design of the ion source has a mirror field of 4 T at the injection and 3 T at the extraction side and a radial field of 2.4 T at the plasma chamber wall. Therefore, the ion beam formation takes place in a strong axial magnetic field. Furthermore, the axial field drops from 3 T to 0.4 T within the first 30 cm. The influence of the high magnetic field on the ion beam extraction and matching to the beam line is investigated. The extraction system is first simulated with the 2D ion trajectory code IGUN with an estimated mean charge state of the extracted ion beam. These results are then compared with the 2D code AXCEL-INP, which can simulate the extraction of ions with different charge states. Finally, the influence of the strong magnetic hexapole field is studied with the three dimensional ion optics code KOBRA. The introduced tool set can be used to optimize the extraction system of the super conducting ECR ion source. ©1999 American Institute of Physics.